This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present techniques. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present techniques. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
Numerical models, referred to as reservoir simulation models or simulation models, may be used to predict performance of hydrocarbon reservoirs. For example, production rates from individual wells may be estimated as a function of time given the well locations and production strategy (rates, pressures at wells, well management information, and the like). Generally, the estimation may be performed by a reservoir simulator, which is a computer program configured to solve equations representing conservation of mass subject to the boundary conditions set at wells and reservoir boundaries. Simulation models are the inputs to the simulator. These simulation models include model parameters within a subsurface model.
Simulation models describe the geometry and properties (such as permeability or porosity, which are the model parameters within the simulation model) of geologic formations that make up the reservoir, the flow and volumetric properties of the reservoir fluids, and the wellbore locations and flow capacities. Simulation models are used to conduct numerical experiments (called simulations) regarding future performance of the field, which are typically used to determine the most profitable operating strategy. For example, the results of simulation may be useful for determining the effects of changing injection pressures, converting injectors to producers, converting producers to injectors, drilling more wells to the reservoir and producing from or injecting to them, and the like.
Improvements to the simulation models may be made by history matching. History matching is the adjustment of the parameters in the simulation models so the predictions of field behavior are consistent with historical production data. As discussed herein, the terms “production data” and “production history” both refer to any data that may be measured over the life of the field. The results of the simulation with the simulation model should be consistent with available production data because this increases the likelihood that predictions of future field behavior are accurate.
A typical process or workflow used in history matching may involve copying an initial simulation model, making some change to that model (adjusting porosity or permeability, for example), running the simulation, and calculating objective function values from the results of the simulation. As discussed in detail below, objective function is a quantitative measure of how well the simulation result matches the historical production data. An example of an objective function is the sum of the error squared over time, where the error is the difference between a field measurement of production rate and the simulation model prediction of the same rate. Perfect agreement between model predictions and field measurements gives an objective function of zero. The process of history matching involves adjusting model parameters to get acceptably low values of the objective function. Once the workflow is specified and parameters that can be adjusted to get a match are identified, optimization algorithms are used to make modifications to the simulation model so the simulation results match with field production data (for example, the simulation results are within a tolerance threshold relative to the production data).
Manual history matching is a time consuming process, highly dependent on the skill and knowledge of a reservoir engineer. As a result, the quality of simulation models produced can be highly variable, depending on the knowledge of the reservoir engineer. By automating parts of the history matching process, the time required to find an acceptable match may be reduced. Further, history matching may be made more systematic by using experimental designs (, systematic exploration of the parameter space) to better understand which parameters influence the match and by using optimization programs to more methodically vary those parameters to improve the match. This is generally termed “assisted history matching” (AHM) and involves developing and automating workflows for history matching and using optimization algorithms to adjust appropriate parameters to improve the match.
Various techniques have been used to assist in history matching. For example, U.S. Patent Application Publication No. 2008/0082469 by Wilkinson, et al., discloses a method for forecasting the production of a petroleum reservoir utilizing genetic programming to construct history matching and forecasting proxies for reservoir simulators. Acting as surrogates for computer simulators, the genetic programming proxies evaluate a large number of simulation models and predict future production forecasts for petroleum reservoirs. A similar optimization technique is disclosed in SPE90307, “Simulation-Based EOR Evaluation of a North Sea Field,” by R. C. Skinner, G. R. Jerauld, and M. D. Bush, which uses genetic algorithms to create multiple history-matched simulation models.
However, a disadvantage of these approaches is the significant number of simulations that have to be performed (in the hundreds or even thousands), which is quite time consuming. For this reason, understanding what parameters affect the match can be difficult and screening the simulation models for geologic consistency can be time-consuming. In addition, running many simulations can involve significant computing resources.
Reducing the number of cells in simulation models by making the cells larger may decrease the computational time for performing these simulations, which allows more simulations to be completed in a short period of time. However, this procedure, termed “coarsening,” may decrease the accuracy of the simulation models by artificially reducing heterogeneity while also rendering models unable to accurately represent large changes in pressure and saturation near wells.
U.S. Patent Application Publication No. 2007/0198234 by Zangl, et al., discloses a method for history matching a simulation model using self organizing maps to generate regions in the simulation model. The method includes: (a) defining regions exhibiting similar behavior in the simulation model thereby generating the simulation model having a plurality of regions, each of the plurality of regions exhibiting a similar behavior; (b) introducing historically known input data to the simulation model; (c) generating output data (for example, performing a simulation) from the simulation model in response to the historically known input data; (d) comparing the output data from the simulation model with a set of historically known output data; (e) adjusting the simulation model when the output data from the simulation model does not correspond to the set of historically known output data, the adjusting step including the step of arithmetically changing each of the regions of the simulation model; and (f) repeating steps (b), (c), (d), and (e) until the output data from the simulation model does correspond to the set of historically known output data. While this method provides a way to parameterize a model, it does not reduce the number of simulations required to be run.
Other approaches to reducing the number of simulations required to obtain a history match have included running a smaller number of simulations and using those results to create a surrogate, often referred to as a proxy or a response surface, for the simulation. See, for example, J. L. Landa, “Reservoir Parameter Estimation Constrained to Pressure Transients, Performance History, and Distributed Saturation Data,” Ph.D. Thesis, Stanford University Department of Petroleum Engineering, (June, 1997); Queipo, et al., “Surrogate modeling-based optimization for the integration of static and dynamic data into a reservoir description,” SPE 63065; Ghoniem, S. A., Aliem, S. A., and El Salaly, M., “A simplified method for petroleum reservoir history matching,” Applied Mathematical Modeling, 8 (August, 1984); and Hoivadik, J. M., and Lame, D. K., “Static characterizations of reservoirs: refining the concepts of connectivity and continuity,” Petroleum Geoscience, 13, 195 (2007). Related information may also be found in U.S. Patent Application Publication Nos. 2007/0027666 and 2007/0198234 and International Patent Application Publication Nos. WO/2007/106244, WO/2006/127151, WO/2005/076124, and WO/2005/074592.
In the surrogate approach, the optimization program may use the surrogate function to search for a history match (for example, indicated by a low value of an objective function), instead of running detailed simulations. Usually the surrogate is a simple mathematical function whose coefficients have been adjusted to fit the response provided by the simulator. The references cited above use several different methods to generate the simulator response. For example, a surrogate may be developed by fitting simple algebraic expressions to the response observed from the simulator, by interpolating between values determined from simulation response using a procedure called kriging, through the use of neural networks, or by spline fitting a simple curve determined by a regression analysis. However, all of these examples involve an empirical expression to represent the simulation response, with no link to the physical process the simulation represents.
As such, the need exists for an enhanced process of assisted history matching. Such a process may include a surrogate that retains some representation of the physical process of flow through the reservoir, allowing for a decrease in the number of simulation runs to improve the results and ease of calculating an assisted history match simulation.
Further related information about assisted history matching may be found in: C. C. Mattax and R. L. Dalton, “Reservoir Simulation,” SPE Monograph Volume 13, (1990); Ewing, R. E, Pilant, M. S, Wade, J. G., and Watson, A. T., “Estimating Parameters in Scientific Computation: A Survey of Experience from Oil and Groundwater Modeling,” IEEE Computational Science & Engineering, 1(3), (1994); W. H. Chen et al. “A New Algorithm for Automatic History Matching,” SPEJ (December, 1971); Z. He and A. Datta-Gupta, and S. Yoon, “Streamline-Based Production Data Integration with Gravity and Changing Field Conditions,” SPEJ, 7, 423-436 (December, 2002); R. W. Schulze-Riegert, J. K. Axmann, O. Haase, D. T. Rian, Y. L. You, “Evolutionary Algorithms Applied to History Matching of Complex Reservoirs,” SPE Reservoir Evaluation and Engineering (April, 2002); Deutsch, C. V., and Cockerham, P. W., “Practical Considerations in the Application of Simulated Annealing to Stochastic Simulation,” Mathematical Geology, 26, 67-82 (1994); Dubost, F. X., Zheng, S. Y., and Corbett, P. W. M., “Analysis and numerical modeling of wireline pressure tests in thin-bedded turbidites,” Journal of Petroleum Science and Engineering, 45, 247-261, 2004; T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods,” SIAM Review, 45, 385-482 (2003); and Queipo et al., “Surrogate modeling-based optimization for the integration of static and dynamic data into a reservoir description,” SPE 63065. Other related information may be found in: Jones et al., Efficient global optimization of expensive black-box functions, Journal of Global Optimization 14, pp 455-492, 1998; and Stern, David, “Practical aspects of Scaleup of Simulation Models,” Journal of Petroleum Technology (September, 2005).